A new transitiometric method of investigation of the solid phase behaviour in asymmetric binary systems was described. Taking the (tetracosane + methane) binary system as a test example the three-phase curve (solid + liquid + vapour) has been determined. The coordinates of the minimum on this transition curve are: T = (317.8 +/- 0.2) K and p = (30 +/- 0.6) MPa. The extension of transitiometric measurements to higher pressures showed that the whole combined transition curve exhibits an inflection point whose coordinates {T = (322.5 +/- 0.2) K, p = (103.8 +/- 0.6) MPa} correspond to the coordinates of the second critical endpoint in this system. Heat flux curves for transitions investigated in ascending order of pressures demonstrated that both melting and the main crystallisation growth are homogeneous processes starting almost at the same equilibrium temperature, but the crystallisation itself starts with a slow homogeneous nucleation in a transient rotator phase a few kelvins above the melting temperature. If experiments are performed in descending order of pressure this transient phase is perturbed, the crystallisation starts from a supercooled state and the respective heat flux curves exhibit two peaks. (C) 2003 Elsevier Science Ltd. All rights reserved.